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We can carry out surveys of customer satisfaction, asking customers if they are happy with the product or service and in what ways these might be improved. At ﬁrst glance, it might look as if, to obtain reliable conclusions which reﬂect the behaviour of the entire customer base, it is necessary to give questionnaires to all the customers. This could clearly be an expensive and time-consuming exercise. Fortunately, however, there are statistical methods which enable sufﬁciently accurate results to be obtained from just a sample of customers.

Essentially we would be making up data. g. some of the answers to a questionnaire), then there are two common elementary approaches to analysis. One is simply to discard any incomplete records. This has two potentially serious weaknesses. The ﬁrst is that it can lead to selection bias distortions of the kind discussed above. If records of a particular kind are more likely to have some values missing, then deleting these records will leave a distorted data set. The second serious weakness is that it can lead to a dramatic reduction in the size of the data set available for analysis.

For example, we might be concerned with just the largest or smallest few – say, the largest 5% – values in the data set. We have already met the median, the value which is in the middle of the data in the sense that 50% of the values are larger and 50% are smaller. This idea can be generalized. e. a quarter) of the data values are larger, and the lower quartile is that value such that 25% of the data values are smaller. Chapter 3 Collecting good data Raw data, like raw potatoes, usually require cleaning before use.